Langmuir 1993,9, 1134-1141
1134
X-ray Interferometry/Holography for the Unambiguous Determination of the Profile Structures of Single Langmuir-Blodgett Monolayers M. A. Murphy* and J. K. Blasie Department of Chemistry and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19104
L. J. Peticolas and J. C.Bean AT&T Bell Laboratories, Murray Hill, New Jersey 07974 Received June 12, 1992. In Final Form: October 26, 1992
X-ray interferometry was used to study the profile structures of Langmuir-Blodgett single monolayer filmsof cadmiumpalmitateand cadmium arachidate"upstroke"-depositedon germanium/siliconmultilayer substratesfabricated by molecularbeam epitaxy (MBE). First, a model refinement analysisof the meridional X-ray diffraction from the bare germaniumlsilicon multilayer substrates was performed, based on the MBE fabrication specifications, to determine their relative electron density profile structures. Second, a highly constrained,real-space refinementanalysis,employingthe thereby known profile structureof the germanium/siliconmultilayer substrate,was used to determine the relativeelectron densityprofile structure of the inorganic multilayer substrate plus the organic overlayer for each fatty acid salt from their respective meridional X-ray diffraction. Last, a real-space refinement analysis was used to determine the absolute electron density profiles of the inorganic multilayer-organic overlayer structures. Separate SiO, and CdSiO, layers lying just below the substrate surface were identified in the profile structures of both samples during the analysis without any prior assumptions as to their nature or existence. The cadmium carboxylate headgroup and methyl endgroup features in the organic monolayer profiles were rather broad in both samples due primarily to a roughening of the CdSiO, layer formed during the monolayer deposition on the SiO, surface of the bare substrate. The so-derived relative electrondensity profiles, which provide information on the average chain configuration length and tilt angle within the Langmuir-Blodgett monolayer, were proven to be correctby X-ray holography where, under appropriate conditions,the profile structure of the organic overlayer is contained explicitly in a specific region of the Patterson function, derived uniquely from the meridionalX-ray diffractiondata from the inorganicmultilayer-organic overlayer without phase informationor model parameters. Thus, X-ray interferometryand holographyare powerful methods for uniquely determiningthe profile structure of both the underlying MBE substrate surface and the organic overlayer(s).
Introduction Organic overlayerscan be deposited sequentially on solid surfacesvia the Langmuir-Blodgett (LB)technique.lt2The most typically studied are LB films of amphiphilic molecules,in particular fatty acids and their salts. Either a single monolayer or multilayer LB films can be formed on a substrate of interest by successive passes of the substrate through the layer of molecules compressed at the air-water interface. These LB films can possess a high degree of structural order both in the layer plane@) and perpendicular to the layer plane(& The characterization of such LB films has been carried out generally on many-layer multilayer films by a variety of experimental techniques. Some of these techniques have been applied to ultrathin multilayer and single monolayer LB films, namely, contact-angle meas~rements,~ Fourier transform infrared (FTIR) spe~troscopy,3~~ near-edge X-ray absorption fine structure (NEXAFS),576 X-ray photoelectron spectroscopy (XPS), infrared attenuated total reflection (1) Blodgett, K. B.; Langmuir, I. Phys. Reo. 1937, 51, 964. (2) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Cas Interfaces; Wiley-Interscience: New York, 1966; Chapter 8. (3) Cohen, S.R.; Naaman, R.; Sagiv, J. J. Phys. Chem. 1986,90,3054. (4) Naselli, C.; Rabolt, J. F.; Swalen, J. D. J. Chem. Phys. 1985, 82, 2126.
(5) Outka, D. A.; Swhr, J.; Rabe, J. P.; Swalen, J. D.; Rotermund, H.
€1. Phys. Reo. Lett. 1987, 59, 1321.
(6) Outka, D. A.; Stchr, J.; Rabe, J. P.; Swalen, J. D. J . Chem. Phys. 1988,88,4076.
(IR-ATR) spectroscopy,7 Fourier transform infrared attenuated total reflection (FTIR-ATR) spectroscopy! scanning tunneling microscopy (STM)? and X-ray diffraction.lOJ1 X-ray interferometry is a powerful method for deriving the profile structure of an unknown monolayer structure placed next to a known multilayer profile structure, as first proposed in 1971.12 This condition can be achieved by depositing the organic monolayer of interest via the LB technique or self-assembly methods upon known, inorganic multilayer superlattice structures made by molecular beam epitaxy (MBE). In this paper we employ this method to derive the profile structure of a single LB monolayer (i.e., the structure as projected onto the surface normal). X-ray interferometryl2 is further coupled with X-ray h ~ l o g r a p h y ,in~ ~which information about the monolayer profile structure can be obtained without any explicit phase information, to prove the so-derived profile structure of the organic LB monolayer unique. (7) Ohnishi, T.; Ishitani, A,; Ishida, H.; Yamamoto, N.;Tsubomura, H. J . Phys. Chem. 1978,82, 1989. (8) Kimura, F.; Umemura, J.; Takenaka, T. Langmuir 1986,2,96. (9) Hbrber,J.K.H.;Lang,C.A.;Hiinsch,T.W.;Heckl,W.M.;Mdhwald, H.Chem. Phys. Lett. 1988,145, 151. (10) Pomerantz, M.; Segmiiller, A. Thin Solid Films 1980,68, 33. (11) Skita, V.; Richardson, W.; Filipkowski, M.; Garito, A.; Blasie, J. K. J . Phys. (Paris) 1986, 47, 1649. (12) Lesslauer, W.; Blasie, J. K. Acta Crystallogr. 1971, A27, 456. (13) Smith, H. M. Principles ofhlolography;Wiley-Interscience: New York, 1969.
0743-7463/93/2409-1134$04.00/00 1993 American Chemical Society
Profile Structures of Single LB Monolayers
Meridional X-ray diffraction data were collected for single monolayer samples of cadmium palmitate (CdP) and cadmium arachidate (CdA) deposited via the LB technique on germanium/silicon (Ge/Si) multilayer superlattice substrates fabricated by MBE. Profile structures for the CdP and CdA monolayers were derived by X-ray interferometry1* and proven correct by X-ray holography.'3 Separate SiO, and CdSiO, layers were identified within these profile structures without any prior knowledge of their existence or nature via these methods. The cadmium carboxylate headgroup and methyl endgroup features in the organic monolayer profiles were rather broad as compared with their counterparts within ultrathin LB multilayers deposited on alkylated s u b ~ t r a t e s , ~due ~ J ~primarily -~~ to the roughness of the CdSiO, substrate surface formed just prior to deposition. The profile thicknesses (average endgroup-endgroup profile length) and endgroup feature profile widths for the two organic monolayers indicated that the CdA LB monolayer contained a relatively high in-plane density ensemble of predominantly all-trans chain configurations uniformly tilted 2 3 O from the normal to the monolayer plane while the CdP LB monolayer contained "patches" of predominantlyall-trans chainswith an averagetilt angle of -Oo. These results were briefly published elsewhere.17
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Met hods The Ge/Si superlattice substrates were fabricated at AT&T Bell Laboratories using a molecular beam epitaxy (MBE) apparatus.Is The substrates were grown on a 4-in. SEH brand Si(100) wafer, N type with resistivities of 0.007-0.020 R cm, according to the following structure: N(Ge,Si,) where N = 3 is the superlattice unit cell number and a = 2 and b = 30 are the number of Ge and Si atomic monolayers, respectively. A (Si:,o) layer was first deposited on the Si(100) wafer to smooth the surface. The subsequent Ge and Si layers were deposited onto the smoothed surface using two electron beam evaporation sources which were separately controlled. Details of the MBE growth were previously reported.I9 The profile thickness of the multilayer superlattice unit cell, (GezSi:,"),is -35.5 A and was chosen to roughly coincide with that of the organic film to be deposited, thereby generating strong X-ray diffraction from this reference structure over regions of photon momentum transfer (or reciprocal) space perpendicular to the substrate plane, i.e., along the q2axis where X-ray scattering from the unknown organic overlayer structure is also strong. By using a small number of superlattice unit cells,N, for the reference structure, one can generate continuous X-ray diffraction over a broad range of q2, allowing for the maximum amount of interference with the scattering from the unknown organic overlayer.20 Also, by making the more electron dense Ge layer to be as thin as possible, one can generate more intense diffraction out to a larger q2for these MBE multilayer substrates as compared to those fabricated via magnetron sputtering described previously.21The Si wafers with this Ge/Si multilayer superlattice on their surface were cut with a diamond dicing saw to provide 1 cm x 1 cm x 30 mil substrates. (14)Skita, V.;Filipkowski, M.; Garito, A. F.; Blasie, J. K. Phys. Reu. 1986,834 5826. (15)Richardson, W.;Blasie, J. K. Phys. Reu. 1989,B39, 12165. (16)Fischetti, R. F.;Skita, V.; Garito, A. F.; Blasie, J. K. Phys. Reu. 1988,B37,4788. (17)Blasie, J. K.;Xu, S.; Murphy, M.; Chupa, J.; McCauley, J. P.; Smith, A. B., 111; Peticolas. L.J.: Bean, J. C. Mat. Res. SOC.Symp. . . Proc. 1992,237,399. (18)Bean, J. C.; Sadowski, E. A. J . Vac. Sci. Technol. 1982,20,137. (19)Bean. J. C.: Feldman. L.C.: Fiorv. A. T.: Nakahara.. S.:. Robinson. I. K.J. Vac..Sci. Technol. 1984,A2, 436. (20) Cowley,J. M. DiffractionPhysics, 2nd revised ed.;North-Holland Publishing Co.: Amsterdam, 1981. (21)Xu, S.;Murphy, M. A.; Amador, S. M.; Blasie, J. K. J. Phys. I 1991,I , 1131. '
Langmuir, Vol. 9, No. 4, 1993 1135 The preparation of the organic monolayers via the LangmuirBlodgett (LB) technique has been previously described" and will only be summarized. Each substrate was thoroughly cleaned with an RBS-35 (concentrated, Pierce) detergent solution and mounted edge-to-edgeonto a 1cm x 1cm glass microscope slide with epoxy for handling purposes to produce a 2 cm x 1cm sized substrate. The arachidic (Aldrich) and palmitic (Sigma) acids had been zone refined with 50 and 70 passes, respectively, at rates of 1and 2.5 cm/h, respectively, and the purity of the center fractions confirmed by differential scanning calorimetry (DSC) measurements on a Dupont 2100 thermal analyzer with a 910 DSC module. A monomolecular layer of either acid was spread onto the clean air-water interface of a Joyce-Loebl Langmuir trough. The subphase was a 0.25 mM CdC12 (MCB Reagents) solution in Milli-Q (Millipore)filtered water with a 0.1 mMTRIS buffer (Sigma) solution of pH -8. The Langmuir films were compressed to a constant surface pressure of 35 and 38 dyn/cm for arachidic and palmitic acid, respectively, and were maintained during deposition. The cleaned Ge/Si portion of the glass plus Ge/Si multilayer superlattice substrate piece was pulled upward through the Langmuir monolayer-water interface at a rate of 3 mm/min to produce a single Langmuir-Blodgett monolayer only on the Ge/Si multilayer superlattice structure. The Langmuir trough system, monolayer film properties, and details of the deposition are further described elsewhere.22 Meridional X-ray diffraction data were collected from these Ge/Si multilayer superlattice substrates, prior to and following the deposition of the LB monolayer on their surface, as a function of qt = (2 sin 8)lX corresponding to elastic photon momentum transfer parallel to the z axis perpendicular to the substrate plane. This meridional X-ray diffraction arises from the projection of the multilayer specimen's three-dimensional electron density distribution along radial vectors perpendicular to the z axis onto the z axis; this projection is defined as the electron density profile for the multilayer specimen. The incident X-ray beam defines an angle (0) with the substrate plane (xy). Meridional X-ray diffraction is observed for w equal to 8, where 2.9 is the angle between the incident and scattered beams. The multilayer specimens were positioned on the w axis of a four-circle diffractometer which was oscillated over an appropriate range of w values, allowing for the collection of the meridional diffraction data over 0.014 A-l < qt < 0.120 A-1with a low-impedance,linear position-sensitive detector (PSD) mounted on the 28 axis and Such meridional diffraction data aligned alongthe qzdire~ti0n.I~ were collected and stored as a sequence of -60-min time frames over a -24-h period from a particular specimen; subsequent examination of arithmetic differences between various pairs of such time frames collected over the -24-h period provided no evidence for any evolution of the specimen's profile structure, as would be expected for radiation damage and other instabilities in the specimen and/or diffractometer system. An Elliott (GX13) rotating anode X-ray generator was used to produce the incident Cu emission spectrum operating at a target loading of 27 kW/mm2. The Cu Kal line (X = 1.541 A) was selected using a cylindrically bent Ge(ll1) monochromator crystal which produced a line-focused X-ray beam at the detector and parallel to the w axis. The specimen to detector distance was 35 cm in helium. The focused X-ray beam width at the detector and the PSD system spatial resolution resulted in a Aqt resolution of -0.001 A-I. The full height of the diffracted line-focused beam was intercepted by the 3-mm-high entrance aperture of the PSD for all diffraction maxima. The full 100-mm active length of the PSD was digitized into 1024 channels by a LeCroy qVt multichannel analyzer. A GPXII Microvax computer (Digital Equipment Corp.) controlled the diffractometer and electronics associated with the PSD. The various multilayer specimens were maintained at 21 O C and in a He environment during diffraction data collection to reduce air scattering.
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Results The total meridional elastic X-ray scattering data for two bare Ge/Si multilayer substrates are shown as ln[1(q,)] in Figure la,c. Subsequently, CdP and CdA LB (22)Blodgett, K.B. J. Am. Chem. SOC.1935,57,1007.
Murphy et al.
1136 Langmuir, Vol. 9, No. 4, 1993
V
possess much smaller amplitude features than that of the Ge/Si multilayer. Thus, we were able to use the known multilayer substrate profile structure as the reference structure to determine the profile structure of the organic overlayers by X-ray interferometry to give the meridional diffraction data for each Ge/Si multilayer plus CdP and CdA monolayers in Figure lb,d, respectively. Following the reference,12 the kinematical meridional X-ray diffraction data for the composite multilayer structures, as shown in Figure lb,d, are given by eq 4, where pki&z)lz
I
I
pkin(qz)12 = pk(qz)I2 + )Fu(qz)I2 + 2pk(qz)lp,(qz)l cos([\kk(qz) - *u(qz)]
- 2 0.01
0.04
0.06
0.08
0.x)
: I 0.01
dA-1)
0.06
0.04
0.08
0.a
dA-1)
Figure 1. Meridional elastic X-ray scattering data, ln[I(q,)l, for (a) bare, three unit cell Ge/Si multilayer substrate, (b) CdP LB monolayer deposited onto (a), (c) bare, three unit cell Ge/Si multilayer substrate, and (d) CdA LB monolayer deposited onto (c). The abscissa is the reciprocal space coordinate, qz (A-l), and the ordinate is the natural log of counts collected. Both (a) and (c) have been offset vertically by 6 units.
monolayerswere deposited on these two substrates, which reaulted in the meridional elastic X-ray scattering data, ln[I(q,)],shown in Figure lb,d, respectively. Our w-oscillations did not extend down to the critical angle for the specular scattering from the multilayer specimens' surface and stopped at the equivalent reciprocal space (qz)min = 0.01 A-I, since we were interested primarily in the kinematical diffraction from these multilayer specimens (see below). For all the specimens studied, meridional X-ray scattering above background scattering levels was observed over the reciprocal space range 0.014 A-1 < q2 < 0.120 A-1 with good signal to noise ratio. For these multilayer systems, the absolute electron density profile, Pab(Z), can be expressed as a sum of two terms shown in eq 2. The mean electron density profile, p(z),extends to P ~ ~ ~=( P(z) z ) +AP(~)
(2)
the multilayer specimedhelium interface and contributes to the meridional specular reflectivity from the specimen which is generally treated in the dynamical diffraction limit, especially for q2 I(qz)crit. The electron density contrast profile, Ap(z), the fluctuation about the mean electron density, gives rise to the kinematical meridional X-ray diffraction over all q z . The resulting meridional elastic X-ray scattering data, I(qz), arising from this absolute electron density profile is shown in eq 3. For qr ptot(qz)l2= pspec(qr)lP + pkin(qz)12
+ wspec(qz) Fkin(qz)
-
(3)
> (QJcrit, ~ s p ( ~ z ) l approaches 0 rapidly and monotonically, and therefore pt.,,t(qZ)l2 pkin(qz)12. Therefore, our meridional X-ray scattering data from these multilayer specimens, I(qz)for (qz)crit < (qzlmin Iqz I(qz)max, is dominated by the kinematical X-ray diffraction data arising from their electron density contrast profile, A&). For our composite inorganic multilayer-organic overlayer system,the Ge/Simultilayer substrate has very sharp, large amplitude features in ita electron density contrast profde, and the Ge/Si multilayer substrate profile structure is essentially known from its MBE fabrication specifications. The organic overlayers represent a small perturbation of the profile structure of the composite system, since their density contrast profiles are anticipated to
+ [2rqzAk,l)
(4)
is the kinematical structure factor modulus squared and pk(qz)12 and pu(qz)12 are the structure factor moduli squared of the known Ge/Si superlattice substrate and unknown LB monolayer, respectively. \kk and 9,are the phases of their respective structure factors (each referenced to the center of mass of their respective profile structure), and Ak, is the distance along z between the center of mass of the Ge/Si superlattice substrate and the LB monolayer. The third term in eq 4 represents the critical interference between the Ge/Si superlattice substrate and the LB monolayer. Ita effect is apparent by direct comparison of the meridional diffraction data for the bare MBE substrates of Figure la,c with the meridional diffraction data for the composite Ge/Si multilayer-LB organic overlayer specimens of Figure lb,d, respectively. The presence of minima in Figure lb,d, which do not exist in Figure la,c, respectively, is a clear indication of the destructive interference effects. The kinematical X-ray diffraction from these composite Ge/Si multilayer-LB organic overlayer specimensranged over only 1order of magnitude for (qz)min 5 q z I (qz)max, due exclusivelyto the narrow width of the Ge features in the profile structure of these Ge/Si multilayer substrates fabricated by MBE. This is a very significant improvement in the resulting signal to noise ratio over this range of qz, in comparison with the X-ray specular reflectivity data from related self-assembled monolayers (SAMs)on uniform siliconwafer substrates.23
Analysis For the analysis presented here, it was assumed that for
qz 2 0.015 A-1, pkin(qz)12 for both the bare Ge/Si multilayer
substrates and the composite Ge/Si multilayer-LB organic overlayer systems could be obtained from their Lorentzby corrected, meridional elastic X-ray scattering, Ic(qz), subtraction of pspeC(qz)12, as approximated by the Lorentzfrom a bare, uniform silicon correctedscattering, [I(qz)]sw, wafer substrate.24 A Lorentz factor of qz was applied, as previously described, arising from the o-oscillationof the specimens.14 This procedure resulted in the kinematical X-ray diffraction from these specimens being confined to the qz range between (qz)min 0.015 A-' and (qz)m= 0.070 A-I. All Fourier analyses, via both interferometry and holography,were thereforerestricted to this qzwindow. X-ray interferometric analysis was performed using a highly constrained, real-space refinement algorithm21to implement the interferometric phasing of the meridional diffractionfrom the Ge/Si multilayer-LBorganicoverlayer system,rather than the point-by-pointphasing in qzspace, (23) Tidswell, I. M.; Ocko, B. M.; Pershan, P. S.; Wasaerman, S. R.; Whitesides, C. M.; Axe, J. D. Phys. Reu. ISSO, 841, 1111. (24) Amador, S. M.; Pachence, J. M.; Fischetti, R.; McCauby, Jr., J. P.; Smith, A. B., 111; Dutton, P. L.; Blasie, J. K. Mater. Res. SOC.Symp. Proc. 1990, 177, 393.
F'rofile Structures of Single LB Monolayers
1
P-11
Langmuir, Vol. 9, No. 4, 1993 1137
I
: 1 -: -200.
-125.
-50.
z (A)
25.
Kx).
-200.
-!25.
-50.
25.
xx).
z (A)
-200.
-125.
-50.
25.
Kx).
2 0 0 . 1 1 2 5 . .
= (A)
Figure 2. Experimentalrelativeelectron density profiles, Apexp-
Figure 3. Half Patterson functions, P ( t ) (a, e), experimental relativeelectrondensityprofiles, Apexp(z)(b, f), derivedvia X-ray interferometry, best model relative electron density profiles, Apm&) (c, g), calculated via double Fourier transform from (d) and (h), respectively, the best model absolute electron density profiles,pm&) (d, h),for CdP and CdA LB monolayer deposited samples, respectively.
as described previously.12 The advantageof this algorithm is that one can avoid several sources of error to which the qz space point-by point phasing is highly sensitive, especially counting statistics errors over regions of qr for which the structure factor for either the known or unknown profile structure is small and errors in the relative scaling of the diffraction data sets employed. To implement interferometric phasing, we must first establish the relative electron density profile for the "known" Ge/Si multilayer substrate. The initial models for the three unit cell Ge/Si multilayer substrates were developed on an absolute electron density scale on the baais of the specifications for their fabrication (see Methods). Electron density levels for Ge and Si were calculated on the basis of the diamond crystal structure with lattice constanta and densities for Ge and Si.25 The initial calculated values for Ge and Si in the absolute electron density scale were 1.41and 0.70 e/A3,respectively, and the thicknesses for Ge2 and Si30layers were 2.31 and 33.25 A, respectively. We then attempted to relax these initial models via a model refinement procedure, utilizing comparisons of the calculated meridional diffraction data and its unique Fourier transform, the Patterson function, for the models with their corresponding experimental meridional diffraction data and Patterson functions subject to the same (qz)min and (qz)m= truncation as described above for the experimental meridional diffraction data. We found it necessary for these particular substrates (whichwere highly unusual by MBE standards,see below) to also employ a highly constrained, real-space refinement analysisz1to guide the model refinement; this procedure utilized a model profile based on the fabrication specifications for only the first two and one-half superlattice unit cells, namely, the (Ge2SisoGe&oGe2) features, as the trial structure. As a result, we were eventually able to refine to the absolute electron density models, pm&), yielding the beat agreement with the experimental meridional diffraction data and corresponding Patterson functions, as shown in Figure 2c,f. Parte a and d of Figure 2 are the corresponding,fully relaxed experimentalrelative electron density profiles, Aperp(z),calculated utilizing the constrained, real-space refinement analysis mentioned above. Parts b and e of Figure 2 are the corresponding
model relative electron density profiles, Apm&), calculated from Figure 2c,f, respectively, via double Fourier transformation subject to the same qz truncation as the experimental diffraction data. By inspection of the features in the region -66 A C z < -10 A in the model and experimental relative electron density profiles, Apm&) and ApeXp(z), corresponding to the Gez/SidSiO,/He features for the bare Ge/Si multilayer substrates, namely, in Figure 2b,a and e,d, we can see that the refined model profile structures for the bare substrates agree very well with the bare substrate profile structures determined experimentallyvia the constrained, real-space refinement. The germanium features in the first two superlattice unit cells of the absolute electron density models are evidently not aa sharp as one would expect ideally from their fabrication specifications; furthermore, the features for the third superlattice unit cell are dramatically different from those anticipated, including the nature of the third germanium feature and the presence of a SiO, surface layer (see Discussion). Therefore, Parts c,b and f,e of Figure 2 represent our initial knowledge of the profile structures for the two bare Ge/Si multilayer substrates that were later used for the deposition of the CdP and CdA LB monolayers, respectively, on their surface. However, since these particular Ge/Si multilayer substrates had already exhibited substantial modifications (of unknown origin at this point) to the third superlattice unit cell at the substrate surface, we anticipated that their surfaces may be subject to some further relaxation and/or modification during LB deposition, the internal structure of these multilayer substrates presumably being the most stable. Therefore, instead of utilizing the entire model relative electron density profile structures of the three unit cell Ge/Si multilayer substrates as our trial functions to initiate the constrained, real-space refinement for the Ge/Si multilayer-CdPand -CdA LB monolayer structures, we used just the interior portions of Figure 2b,e, containing only the Ge feature peaks and the Si features of the first two and one-half superlattice unit cells on the left and omitting the surface Si/SiO, layer features including the derivative-like feature on the right corresponding to the SiO,/He interface,i.e., the profile structure, indicated with arrows in Figure 2b, of only the (Ge2Si~Ge2Sid3ez) portion of the final reference Ge/Si multilayer profile structure. Parte b and f of Figure 3 contain the experimental relative
( 2 ) (a, d), derived via X-ray interferometry,best model relative electron density profiles, Ap,,,&), (b, e), calculated via double Fourier transform from (c) and (0,respectively, and best model (c, f), for bare, three absolute electron density profiles, p,&) unit cell Ge/Si multilayer substrates, later used for CdP and CdA monolayer deposition, respectively.
(25) Ashcroft, N. W.; Mermin, N. D. Solid State Physics; Holt,Rinehart and Winston: New York, 1976; Chapter 4.
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1138 Langmuir, Vol. 9, No. 4, 1993
electron density profile structures, Ape&), for the composite Ge/Si multilayer-CdP and -CdA LB monolayer structures, respectively, so-derived from their meridional X-ray diffraction data applying the highly constrained, real-space refinement.21Following deposition of the CdP and CdA LB monolayerson the surfaceof these multilayer substrates, additional, more complex features appear at and beyond the profile position of the SiO, surface of the substrates for -28 A < z < 19 A. To understand the nature of these new features and the other additional features in the organic overlayer region of these experimental relative electron density profiles, it is necessary to establish realspace, absolute electron density profile models that will account for all the individual features in Figure 3b,f. Parts d and h of Figure 3 are the refined absolute electron density profile models for the CdP and CdA LB cases, respectively. Their correspondingmodel relative electron density profiles are shown in Figure 3c,g, respectively. These model relative electron density profiles were produced by first Fourier transforming the absolute electron density profile model to get the model profile's kinematical structure factor. We then applied the experimentalvalues for the (qr)minand (qr)max truncation, and performed an inverse Fourier transform of the model profile's kinematical structure factor to obtain the model relative electron density profile. This procedure was earlier referred to as a double Fourier transform, with the qztruncation window employed. We then refined the model profiles until their model relative electron density profiles were almost identical to the experimental relative electron density profiles in Figure 3b,f. In this real-spacemodel refinement, we found that each feature in the absolute electron density profile model has a 1:l correspondencewith ita counterpart in the model relative electron density profile, in both position (*0.1 A) and density level (fO.O1 e/A3). We thereby established that, in the model relative electron densit profile structures, the four peak features at z = -120 z E -88 A, z = -75 A, and z E -60 A arise from the three separate Gez layers (the last being split) for CdP in Fi re 3c, the three peak features at z = -120 A,z = -82 , and z E -60 A arise from the three separate Gez layers for CdA in Figure 3g, the features within the region -50 A < z < -24 A uniquely arise from the Si/SiO,/CdSiO, layers in the vicinity of the substrate surface, and the features within the region -13 A < z < 22 A uniquely arise from the CdCOO/(CHz)n/CHBportions of the CdP and CdA LB monolayers (seeDiscussion). Hence,these refined absolute electron density profile models provide us with a rather precise knowledge of the profile structures of the compositeGe/Si multilayer-LB organicoverlayer systems.
r
Discussion The highly constrained,real-spacerefinementalgorithm provides one solution of a finite number of solutions for the phase of the kinematical structure factor, using the phase dominanceof the known reference structure to force the box-refinement algorithm to converge to the local structure solution closest to the trial structure.?6.n In order to prove the correctness of the so-derived, experimental relative electron density profiles described above, the method of X-ray holography was used in which the profile structure for the overlayer can be made to be contained ~ unique explicitly in the Patterson function, P ( ~ 1 . lThe Fourier transform of the kinematical structure factor modulus squared, without phase information, yields the (26) Stroud, R. M.; Agard, D. A. Biophys. J . 1979,25,495. (27) Makowski, L. J . Appl. Crystallogr. 1981, 24, 160.
Patterson function, P(z), namely, the autocorrelation function for the relative electron density profile structure, ~ p ( z ) . 1 ~ -That ~ 8 P(z)is the autocorrelation of the relative, and not the absolute, electron density profile (i.e., Ap(z) vs pa,,&), itself) is a simple consequence of the truncation of the meridionaldiffractiondata for qr < (q2)min mentioned in the Analysis. Performing an inverse Fourier transform of eq 4 provides the half Patterson function for the profile structure of the composite Ge/Si multilayer-LB organic overlayer system given in eq 5, where an asterisk denotes Pt,,(r?lo)= Pk(Zl0)+ P,(zlo) + APk(-Z)
* AP,(Z) * 6(z -
(5)
the convolution operation. Pk and P, are the autocorrelation functions of the known multilayer substrate relative electron density profile, Apk(z), and unknown organic overlayer relative electron density profile, Ap,(z), respectively, occurring about z = 0 A in P(z). The third term in the sum is the cross-correlation function between the known and the unknown relative electron density profile structures shifted to z = Aku (see Results). If the known multilayer substrate reference profile structure is chosen such that Apk(Z) = 6(z), a 6 function, and Aku is larger than the longest z-translation vector in the autocorrelation of the known structure and in the autocorrelation of the unknown structure, then the half Patterson function for the profile structure of the composite system contains explicitly only the relative electron density profile of the unknown overlayer structure itselfin the proximity of Aku, i.e. Pt,t(z=Ak,) = AP,(Z)
* 6(2) = AP,(z)
(6)
This approach is simply off-axis Fourier holography, in which the unknown structure itself is uniquely reconstructed in this particular region of the Patterson function, obtained via a unique Fourier transformation of the h0l0gram.l~ We can use this approach to prove that the relative electron density profile structures of the organic overlayers derived above via X-ray interferometry are indeed correct. Parts a and e of Figure 3 are the half Patterson functions of the three-bilayer Ge/Si substrate plus the CdP LB monolayer and the three-bilayer Ge/Si substrate plus the CdA LB monolayer, respectively. Parts b and f of Figure 3 are their corresponding experimental relative electron density profiles derived via X-ray interferometry. The Patterson functions are aligned with their corresponding relative electron density profile structures such that the origin of the Patterson function is located at the same z axis position as the first Gea peak feature at the left edge of the corresponding relative electron density profile. By inspection of the features in the Patterson functionsand in the correspondingexperimental relative electron density profiles over the region -48 A < z < 22 A,it is readily apparent that the Gez peak features at the left edge of the experimentalrelativeelectron density profile (which approximates a 6 function) is convoluted with the organicoverlayer features at the right edge of the profile in the region -48 8, < z < 22 A to reconstruct the latter's features in the Patterson function over the same region. This nearly identical degree of agreement between the features at the edge of the finite-extent Patterson function for -48 A < z < 22 A and those features at the edge of the experimental relative electron density profile due to the LB organicoverlayer indicatesthat the overlayer (28) Fischetti, R. F.; Filipkowski, M.;Carito, A. F.; Blasie, J. K. Phys. Rev. 1988, B37, 4714.
Profile Structures of Single LB Monolayers
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Langnuir, Vol. 9, No. 4,1993 1139
h
01
x
-0.
-a. -XI. z (A)
0.
x).
-EO.
-m.
-w. (A)
0.
SQ.
=
Figure 4. Model absolute electron density profiles, pm(&), for (a, c) bare, three unit cell Ge/Si multilayer substrates (b, d) CdP and CdA LB monolayer deposited samples, respectively.
profile structures derived via X-ray interferometry are thereby proven correct by X-ray holography. In order to understand all the various features present in the relative electron density profiles exhibiting the effects of transform truncation at both (&,in and (qr)mar, as shown in Figures 2a,b and d,e, and 3b,c and f,g, it is necessary to first examine their respective absoluteelectron density model profiles. The best absolute electron density model profiles for the bare GeISi multilayer substrates employed in this study are shown in Figure 4a,c. In both cases, the substrate had undergone substantial changes, especially within the third superlattice unit cell adjacent to the substrate surface, as compared with the MBE fabricationspecifications [these particular substrates were highly unusual by MBE standards; of the many such substrates that we have examined, these were the only substrates whose profile structures differed significantly from the fabrication specifications;see refs 17 and 31 for example]. The third Ge2 peak nearest the substrate surfacehad shifted in position and broadened considerably, presumablydue to the relaxation of the Ge/Si interfaces;29 thesharpsteplikefeaturefor-46A< z
